Friday, May 23, 2014

Finding sea ice underside melting at any time

~ A refraction discovery is dwarfed by its much larger data application.  
~ Observing underside melting will help understand sea ice dynamics.  

 From the fascinating revelation of actually observing whether the underside of sea ice is melting or not.  We can can take it to a  much larger scale,  to the space platforms.   Where the thawing action is visible whenever they display their daily average temperature results. At first glance, it may surprise some,  the underside overall melts in a wide section  one day,  then to another area much further away the next,  leaving the impression of chaos which if you go underwater at the North Pole,  you would see just that,  underside art of mix geometry and light,  art only nature can achieve.

Refraction Discovery …

THIN SEA ICE  horizon

     Going back to several articles on EH2r,  sketches are needed to explain how we can see what is going on under more than hundred of centimeters of ice.   First we must observe what happens during Arctic Ocean late fall,  nascent sea ice sheet grows quite rapidly:

Super accretion
Tw : temperature of top of sea water;   Ti: top of sea ice temperature;   Ta :   air surface temperature.

 In Arctic autumn,  with  new sea ice just formed, thermal fluxes are aligned upwards to space.  Sea ice thickens quickly in direct relation to Ta,  surface Air Temperature,  the colder surface air is, the faster ice accretes .   In late fall , Ta is coldest of the mediums.  Conduction from either sea water and ice  go upwards just alike.   Adiabatic convection affects the cooling process accelerating it much further.  This gives super accretion optically seen by the lowering of the horizon:

Super accretion mirages of the freshly formed sea ice,  the horizon is dramatically low,  because new sea ice is quite warmer than the air just above.   The horizon line should be on top of the grey cloud like layer, right under is the refracted sky by an inferior mirage.


     After the start of the long Arctic night,  where sea ice thickness exceeds 50 cm,  thermal flux to space is not as strong when cloud free,  as the ice thickens, absent sun makes top of sea ice largely always colder than surface air,   surface to air adiabatic lapse rates with thin ice turns to stable isothermal layers.  A near permanent thermal inversion  exists.  Up to hundreds of meters above ice in darkness,  the air subsists almost always warmer,  but does nothing but cooling.   The horizon at that time is almost always much higher than fall [unless fall time has a rare huge influx of warm air temperatures].   Surface air temperature colder than top of ice is a super accretion event of late fall, theoretical possible with winter thick ice (by cold air advection).   However,  I have very few observations of the lower horizon during darkness (most are caused by low clouds).   Therefore super accretion with thick sea ice is a very rare or unlikely event.    No atmospheric adiabatic convection along with less long wave radiation escaping to space slows sea ice accretion.  With numerous cumulative days in darkness,  top of sea ice becomes coldest  making a progressively thicker coldest strata from top towards bottom.   Much warmer air can only be found higher above,  from its peak in warmest temperature a stable near continuous inversion is made which has a profound impact in slowing further extreme cooling of sea ice. The equivalent to thick sea ice insolation exists invisibly but not near the horizon:

Near permanent inversion leaves the horizon risen throughout the dark season,  only lowered by low clouds.   Sea ice has a totally different look,  its white instead of dark,  snow also covers most of its surface.   The height of the horizon varies according to the lapse rate ,  a calculation:

    Horizon Height is directly proportional to the difference in temperature between Ta and Ti.   The colder Ti the higher the horizon,  like the example above. 

Moderate accretion happens by the shear thickness of the ice, now a large insulator,  thermal flows upwards towards space are similar to the fall scenario except less heat escapes,  more often than not,  it is the top of the ice which is the coldest medium, the difference in temperature between very near ice air may be small with gradual warming further aloft.  Cooling of air near the ice adds a downward thermal flux, but since air has significantly less heat capacity,  the ice absorbs a fraction of this long wave heat but does not warm up much from the gain and re-emits thermal rays towards space.   Unlike during Autumn,  the thicker colder ice layer causes accretion.

      These sketches are done without the presence of clouds in mind.   Thermal flows dramatically change when low overcast cloud conditions exist, when so,  sea ice horizon height lowers similar to effects by the noon sun.  In addition to a cold on top and warm ice strata below, a thinner top of ice temperature variance zone always susceptible to weather must be common.   But the net effect of the long Arctic night creates a large coldest ice layer which becomes steep in proportion to the severity of winter degree days, accordingly,  spring  season onwards sea ice requires significant warming before the structure of the lower Arctic Ocean atmosphere changes more permanently. 

Return of the sun

       In Early Spring, Ice Thickness depends on how long night climate conditions were.    But more than 100 cm First year ice , as usually measured throughout the Arctic at winter sunrise, has specific thermal properties in relation to depth which changes diurnally.  A coldest temperature layer lurks near top of ice,  but when sunny,  is found deeper above sea ice centre column.  When evening occurs, top of ice cools by short lived adiabatic convection,  the coldest layer just below ice surface accelerates the re-cooling strangely faster than the lower specific heat capacity of air.  Top of ice and subsequently the air right above cools,   this gives the sea ice rising horizon diurnal effect in a cloud free atmosphere:

     Left picture horizon was lowered from solar ray battering,  layers of the near and gradually more distant horizon appear to grow on top of each other until they form an ice wall (center and right).  Ice is warmest after Local Apparent Noon,  coldest in the morning prior to sunrise and for a few hours after.  This rising horizon simply indicated that the top of sea ice was only partially warmed, as the sun lowered,  cooled fast by convection  and contact conduction by the larger much colder ice layer immediately under.  Surface air  cooled less as rapidly,  but only very near top of the ice first,  then upwards in altitude. 

    In the evening after a sun ray bath,  top of ice appears to cool fastest.   From a starting point of surface air and top of sea ice having the same temperature,  the lowest air stratum in direct contact cools along with sea ice,  causing readily visible thermal layering which becomes the famous Norse "ice wall".   This "wall" becomes higher as the inversion becomes steeper at the ice surface to air interface.  The inversion peak also rises in altitude,  this makes "ducting",  a refraction phenomenon similar to fibre optics, possible at higher above the horizon.  Accretion continues in such  a time of day,  but much weaker,  because the ice is thick and was warmed by earlier solar heating,  a bottom refreeze can make this accretion unnoticeable. 

After Local Apparent Noon Melting of sea ice  

Here is where an horizontal observation is linked to satellite data,  after a few hours exposure to sun rays,  the ice horizon lowers until bottoming at the true astronomical horizon:

    About 2 hours after Local Apparent Noon , April 10 2014,  the horizon is at its lowest point.  Top of ice warmed no more,  the horizon stayed fixed,   underside of ice melting has occurred for about an hour.  

   As seen from the refraction largely nullified,  the ice horizon is at the same height as with open sea water in autumn when the temperatures between sea and surface air are the same.   Ti = Ta  means there is very little or no more loss of thermal heat from sea to space,  especially since short wave heat is added to the ice by the sun warming  its top layer.  The coldest ice layer shrinks,  more thermal heat from sea water is focused on the bottom of the ice.  The  underside melts until  very top of sea ice becomes coldest again. The reason for the temperature stalemate is found with the latent heat of melting at bottom.  Excess heat can't increase temperature because excess heat goes to melting ice. 

Applied formulas

   Since sea ice can have 2 distinct surface to air attributes;   very warm air above the freezing point of sea ice does not need much consideration whether the surface to air profile is adiabatic or stable.  Any underside melting formula should be adjusted accordingly .   The summer formula:  

    Ta >= Ti  hypothetical formula for determining where thick sea ice underside melts. Applies when Ta is equal or greater than -1.8 C .

         If the average surface temperature is greater or equal to the average temperature of top of sea ice,  its underside melts because thermal rays no longer escape from sea towards space.  3 meter sea ice bottom also melts for the same reason.  Even melting thicker sea ice just as much.    According to many buoy data,  the bottom of the ice column temperature  is nearly the same to adjoining sea water.   The process of accretion,   which exists when top of sea water thermal rays escape to space,  adds more ice onto the underside,   but when there is no longer any heat escaping,  ice bottom melting should start.   

          When the daily average temperature  of surface air exceeds or equals top of  ice average temperature,  there is an overall net melting of sea ice. Thickness loss is not seen above on the surface aside from the snow which appears to sublimate and becoming more porous.   At any given day with good satellite data,  we can observe where the melting occurs. Apparently it varies with the weather towards the centre of the Arctic Ocean.  Applying the formula to satellite data charts,  we can clearly delineate Arctic Ocean pack adjoining open water where  temperatures  of air and sea ice match,  obviously there is melting along sea ice shores: 

University of Maine excellent daily temperature averages of both sea ice top and surface air can be joined or superimposed to reveal where Ta is greater or equal to Ti:

A confirmation of sorts can be seen,  I traced by hand where Ta is >= Ti in black.  Of Course, Arctic Ocean sea ice shorelines must have underside melting especially at this time of the year.   What is most interesting are the long segments of apparent melting deep towards the North Pole.  These are weather related, as with weather, they are not consistent until  overwhelming heat takes charge of the Arctic:

A few days later and Hudson Bay underside sea ice appeared  completely melting.  But note Central Arctic Ocean melt zones with a totally different look.  This is not surprising.  But a long time chart of underside melting averages may be interesting.  

During early Polar spring days (Ta < -1.8 C), the melting period lasts as long as Ta = Ti. After the long night sunrise, the melting period gradually increases day by longer day by solar rays increasing in power with the sun rising in altitude.  Despite sea ice albedo and or reflection of rays back upwards, there is a significant enough absorption of solar rays to warm up top of sea ice to change thermal flux pattern diurnally. 

At lower surface temperatures than -1.8 C, the formula Ta = Ti maintains an isothermal interface, in such instances top of ice has a net positive or downward thermal flux towards the coldest layer, sea ice underside can melt even during the presence of very cold surface temperatures. (Ti > Ta has not been optically observed with thick ice with clear air ).

     A totally new perspective of analyzing sea ice optically has important features which become even grander when taken to a much larger scale. From all available data to date, the underside of sea ice melts when sea water thermal flux loss towards space becomes cut off by surface heat input either by the sun or by clouds. Low clouds resends lost Long Wave Radiation towards the surface, obviously this heat feedback is not as strong as high sun warming, studying the cloudy horizon has many pitfalls related to low contrast resolution. I suspect low clouds, a feature of warmer Arctic weather may contribute to much slighter bottom melting or certainly a stop of accretion, as long as surface temperatures are equal or higher than top of sea ice, in this case warmer air matters more.  Arctic Ocean  summer season of 2013 had more underside thawing than from the sun, extent and area was muddled by the lack of sea ice compaction by the extensive presence of cloud laden cyclones,   nevertheless a significant minimum was achieved.  

      Hypothetical proof:

      Observation data can prove underside melt despite lack of actual high resolution measurements.    Phase change is key, it takes energy to melt ice,  but when it freezes there is a release of latent heat.  This latent heat of fusion should reverse the cooling of top of sea ice, hence it should be seen lowering the horizon again.  A clear  day on April 24 2014 with the right conditions showed exactly this:

                                               Time        horizon
  LAN                             2.97      
+ 1 hr 1 min 3.37
+3 hr 09                   3.69
+ 4 hr 30 3.14
+5  hr 49 4.43
 +6 hr 25 4.25
+7 hr 31 4.58
    + 8 hr 3 min  4.89

   At local apparent noon the ice horizon was 2.97' above a fixed point.  1 hour later, 3.37 minutes of arc, and so it should rise without interruption given the clear day.  Not so,  the horizon rose in steps, as often does on clear days, so for hour 4.5  sun rays significantly less hot can't lower the horizon.   Same at hour 5 49 min.   Another possible candidate of heat is the air next to ice loosing heat to the colder ice layer.   But 1 joule of heat loss of air (about 1 C cooling) transposes to top of ice at about +.25 joules.  While 1 cm of sea water at 1 meter square weighs 10 Kg,  that is 3340 kiloJoules per meter square released upwards.   There has to be such diurnal steps. 

WD May 25, June 5-11 2014